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Queensboro Bridge 




REPORT ON 

i 

DESIGN AND CONSTRUCTION 


WILLIAM H. BURR, Consulting Engineer 
BOLLER & HODGE, Consulting Engineers 


1908 




Queensboro Bridge 


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REPORT ON 

DESIGN AND CONSTRUCTION 


WILLIAM H. BURR, Consulting Engineer 

ir 

BOLLER & HODGE, Consulting Engineers 


1908 








* 




MARTIN B. BROWN 


* PRESS * 



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Wm. H. Burr, 

Consulting Engineer, 

Broadway and One Hundred and Seventeenth Street. 

New York, N. Y., November 4, 1908. 

Hon. J. W. Stevenson, 

Commissioner of Bridges, 

City of New York. 

Dear Sir —Pursuant to action of the Board of Estimate and Appor¬ 
tionment, you instructed me, under date of June 9, 1908, “ to examine and 
report upon the design and structure of the Blackwell’s Island Bridge.” 
Since that date I have been continuously prosecuting the work covered 
by your instructions and I respectfully submit this as my report. 

I understand your instructions as to this examination to be sufficiently 
broad to include the general questions of safety and stability irrespective of 
the provisions of the specifications; in other words, that this examination 
is not to be limited by those provisions. 

On taking up these duties I found that a part of the engineering staff 
of the Department of Bridges had for some time been engaged on a re¬ 
computation of the stresses of the Blackwell’s Island Bridge; but in order 
that the duties prescribed to me might be completed as an independent and 
homogeneous whole, a complete analysis of the stresses in the Blackwell’s 
Island type of bridge structure was made as set forth in Appendix I., in 
accordance with which an independent set of computations of stresses for 
the entire structure was begun and carried to> completion. The results of 
the computations on which the conclusions of this report are based are given 
on sheets 1, 2, 3, 4, 5 and 6, appended hereto. 

The Blackwell’s Island Bridge structure is of the cantilever type, but 
without the usual suspended span between the extremities of the cantilever 
arms. The total length of the structure, exclusive of the approaches, which 
are not covered by this examination and report, is 3,724.5 feet, comprising 
2 shore or anchor spans 469.5 feet and 459 feet long, respectively; 2 river 
or cantilever spans of 1,182 feet and 984 feet, respectively; and 1 island 


4 


span 630 feet in length. The width of the bridge from centre to centre 
of the two trusses is 60 feet. The omission of the ordinary suspended 
span between the cantilever arms necessitated the employment of so-called 
rocker arms or vertical members, having a length equal to the depth of 
truss and connecting the extremities of the top chords of the island canti¬ 
lever arms with the extremities of the bottom chords of the other canti¬ 
lever arms in the same span, thus making the trusses continuous through¬ 
out the entire distance from the Manhattan anchorage to the Queens Bor¬ 
ough anchorage. 

The contract for the superstructure of this bridge was awarded to the 
Pennsylvania Steel Company and executed on November 20, 1903. The 
entire steel work was manufactured and put in place by that company. The 
design as modified to accommodate four elevated railway tracks was com¬ 
pleted in 1904. 

Nickel steel was specified to be used in the eye-bars and pins of the 
top chords and diagonal tension members as might be ordered or approved 
by the Commissioner, and that metal was so used. All other parts of the 
structure except some small special cast iron items were of ordinary carbon 
structural steel. 

The chemical requirements for these two grades of steel are taken as 
follows from the specifications: 

The physical requirements of the same two grades of steel are also 
taken from the specifications as follows: 


CHEMICAL REQUIREMENTS. 

NICKEL STEEL. 



Phosphorus. 

P.c. Max. 

Sulphur. 

P.c. Max. 

Nickel 

P.c. Min. 


Basic. 

Acid. 

Eye-bars and Pins. 

.04 

.06 

.05 

3.25 



STRUCTURAL STEEL. 


Plates, Shapes, Bars and Pins. 

.04 

.08 

.05 


Rivet Steel. 

.04 

.04 

.04 


Steel Castings. 

.05 

.08 

.05 



































PHYSICAL REQUIREMENTS. 

Specimen Tests. 

NICKEL STEEL. 




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7 


The original design of this structure contemplated but two elevated 
railway tracks, as the original specifications called for the following 
“ congested ” live load of 12,600 lbs. per linear foot of bridge: 


2 Elevated Railway Tracks, at 1,700 lbs. p. 1 . f. 3400 lbs. 

4 Trolley Railway Tracks, at 1,000 lbs. p. 1 . f. 4,000 lbs. 

35.5 ft. roadway, at 100 lbs. per sq. ft. 3,550lbs. 

2-11 ft. sidewalks, at 75 lbs. per sq. ft. 1,650 lbs. 


12,600 lbs. 

A “ regular ” live load of one-half of the above, i. e., 6,300 lbs. per 
lin. ft. of bridge was further specified. In consequence of adding two 
more lines of elevated railway to the capacity of the bridge in Septem¬ 
ber 1904, the preceding “ congested ” and “ regular ” loads were increased 
to 16,000 lbs. and 8,000 lbs. respectively. 

The manner of using these two classes of loads, as well as the wind 
loading and certain other load concentrations, for determining the 
stresses in all parts of the structure is prescribed in the specifications as 
follows: 

For the main members of the trusses and the towers: 

(A) A load of 8,000 pounds per lin. ft, of bridge as “ regular,” or 

(B) 16,000 pounds per lin. ft. of bridge as “ congested ” traffic. 

For the secondary members of the trusses, the floor beams and the 

floor system: 

(C) On each of the four elevated railroad tracks a load of 52 tons 
on 4 axles, 6 ft. plus 10 ft. plus 6 ft. apart (the motor ends of 2 motor cars of 
the Interborough Rapid Transit Co.) 

(D) On each street car track either a load of 26 tons on 2 axles 
10 ft. apart or a load of 1,800 pounds per lin. ft. of track. 

(E) On any part of the roadway a load of 24 tons on 2 axles 10 ft. 
apart and 5 ft. gauge (assumed to occupy a width of 12 ft. and a length 
of 30 ft.), and upon the remaining portion of the floor a load of 100 
pounds per square foot. 

* 

(F) On the footwalks a load of 100 pounds per square foot. 

(38) The wind pressure shall be assumed as a static load of 1,000 lbs. 
per lin. foot and an additional moving load acting in either direction 
horizontally with 1,000 pounds per lin. ft. 






8 


\ 


For the proper proportioning of the parts of the structure, the fol¬ 
lowing greatest permissible unit stresses in lbs. per sq. in. were provided 
for the various parts of the structure indicated. 


For Dead Load 
and Regular 
Live Load or 
for Dead Load 
and Wind. 


For Dead Load 
and 

Congested 
Live Load. 


Pounds per Square Inch. 


a) For Nickel Steel in Eye Bars and Pins— 

Tension. 

Shear on pins. 

Bearing on diameter of pins. . 

Bending on outer fiber of pins. 

( b ) For Structural Steel in Main Members of Trusses, Towers and 
Bracing— 

Tension. 

Compression. 

Shear on shop rivets, bolts and pins. 

Bearing on diameter of shop rivets, bolts and pins. 

Bending on outer fiber of pins. 


30,000 

20,000 

40,000 

40,000 

20,000 

P 

20,000-90- 
13,000 
25,000 
25,000 


39,000 

24,000 

48,000 

48,000 

24,000 

1 

24,000-100- 

r 

16,000 

30,000 

30,000 


* 


(c) For Structural Steel in Secondary Members of Trusses— 


Pounds per 
Square Inch. 


Tension in subverticals (hangers).1. 

Compression in subdiagonals. 

Shear on shop rivets and bolts. 

Bearing on diameter of shop rivets and bolts. . 

(d) For Structural Steel in Floor System of Roadway and Footways and in all Floor 
Beams— 

Tension chords. 

Shear on shop rivets, bolts and web-plate net section. 

Bearing on shop rivets and bolts. 

(c) For Structural Steel in Floor System (including brackets) for Railroad and Trolley 
Tracks— 

Tension chords. 

Shear on shop rivets, bolts and web-plate net section. 

Bearing on shop rivets and bolts. 


18,000 

1* 

18,000-80- 

r 

12,000 

24,000 


15,000 

10,000 

20,000 


10,000 

7,000 

14,000. 


C 


* Where 1 = length and r=least radius of gyration both in inches. 

A reduction in unit stresses must be made for all members not vertical, to allow for outer fiber 
stresses caused by the bending of the member under its own weight. 


% 











































9 


Further provisions for the proportioning of parts required in this 
examination are: 

Members subject to reversals of strains shall be proportioned for 
each kind of strain, and the section shall, be determined by the strains re¬ 
quiring the greater net area. 

For combined strains due to dead load, ‘ regular ’ live load and wind, 
the unit strains given above may be increased 20 per cent. 

“No compression member shall have a length exceeding 100 times 
its least radius of gyration, excepting those for bracing, which may have a 
length not exceeding 120 times the least radius of gyration.” 

The remaining provisions of the specifications need not be quoted for 
the purposes of this report, but they are reasonably full and comprehensive 
and well calculated to accomplish the ends desired. 

The transverse bracing of this bridge is designed to transfer all wind 
load against the upper part of the structure to the lower chord. All wind 
truss stresses will therefore be found in the plane or surface of the latter. 

These specifications were prepared for the design of a bridge structure 
of unusual magnitude, the greatest length of span being 1,200 ft., and the 
volume of traffic to be accommodated is of extraordinary proportions. Fig. 
1 shows a skeleton elevation of the entire structure between the Manhattan 
and Queens Borough anchorages. Fig. 2, on the other hand, shows a 
typical cross-section of the bridge as contempated under the specifications. 
The bridge has two decks or traffic carrying platforms, one along the lower 
chord accommodating four trolley railway tracks, )two outside of the 
trusses and two inside adjacent to those trusses, with a 35.5 ft. roadway 
between the latter. The upper deck was intended under the specifications 
to accommodate four lines of elevated railway track between the trusses and 
two sidewalks, each 11 ft. wide, supported on cantilever brackets outside 
of the trusses. 

As there are no elevated railway connections at the Queens Borough 
end of the bridge and no immediate prospect of such connections, the 
bridge will not be required to carry any elevated railway traffic for some 
indefinite period after its completion. Furthermore, it is still more un¬ 
certain when the growth of traffic which this bridge must accommodate will 
require the use of four railway tracks on, the upper deck. It was decided 
therefore to place in position the stringers only of those tracks for the 


IO 


present and to use the pair adjacent to each truss to support the sidewalk* 
and thus save the overhanging cantilever construction of the latter out¬ 
side of the trusses, until the bridge should be required to carry full elevated 
railway traffic. The condition under which the bridge would be completed , 
therefore, is shown by the typical cross-section, Fig. 3. 




* 


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13 



BLACKWELLS island bpsdcl. 

Scale 2. in. *25 "Ph 

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Scale 2. ln. c 25 "Ph 


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4 











17 


Propei provision for various classes of loading for a structure of 
such magnitude, designed to carry an extraordinary volume of traffic, 
with the corresponding working* stresses, is largely a matter of judg¬ 
ment. d his broad question was given much consideration by a Com¬ 
mission of Biidge Experts, appointed to examine and pass upon the 
plans for the Manhattan Bridge, under date of March 9, 1903. The Man¬ 
hattan Bridge was planned for the same total traffic capacity as that of 
the Blackwell s Island Bridge, and that Commission recommended the 
same “congested” and “regular” loads of 16,000 lbs. and 8,000 lbs. 
per lin. ft. of bridge as prescribed for the Blackwell’s Island Bridge. 
That Commission, consisting of Messrs. George S. Morison, C. C. 
Schneider, Mansfield Merriman, Henry W. Hodge and Theodore Cooper, 
stated, however, that the “ congested ” load “ is a possible load which 
could never occur unless special pains were taken to produce it.” With 
such an improbable but possible load, the working stresses may prop¬ 
erly be taken substantially higher than for a “ regular ” load, which, 
while not likely to exist frequently, is far more likely to occur than the 
“ congested.” This Commission of Bridge Experts made no recom¬ 
mendation as to working stresses for the “ congested ” load, but stated 
“ that the bridge should be so proportioned that with the ‘ congested ’ 
load of 16,000 lbs. per lin. ft., covering the whole bridge, combined with 
dead load and wind pressure, no stresses would be produced anywhere 
reaching the elastic limit of the material. * * * In other words, it 

should not be possible for such an extraordinary ‘ congested ’ load to do 
any permanent injury to the bridge.” 

Inasmuch as actual tests of full size annealed eye-bars of both 
ordinary structural and nickel steel have shown that the elastic limits of 
those members may be safely taken at about 28,000 lbs. per sq. in. and 
48,000 lbs. per sq. in., respectively, it will be found that the prescribed 
working stresses under the congested live load in the specifications 
of the Blackivell’s Island Bridge lie within the prescribed limits set forth 
by the Commission of Bridge Experts named above. In fact, it appears 
from the latest tests of full size carbon structural steel and nickel steel 
columns that the greatest prescribed working stresses for the compres¬ 
sion members of the Blackwell’s Island Bridge lie sensibly below those 
limits. It appears from a careful reading of the report of this Commis- 


1 8 


sion in connection with the specifications for the Blackwell’s Island 
Bridge that the latter were modelled closely upon the lines laid down in 
the report of the Commission of Bridge Experts so far as they were 
applicable to the Blackwell’s Island structure. 

While therefore the specified loads and working stresses for the 
Blackwell's Island Bridge are to be considered as safe and satisfactory 
in the light of knowledge and precedent available when they were drawn, 
it is my judgment, that the experience which has accrued in connection 
with the actual construction of long span bridge structures within the 
intervening five years is such as to require some modification of the high 
working stresses then thought permissible. I cannot concur in the 
opinion of the Commission of Bridge Experts, that a possible combina¬ 
tion .of loads should be permitted to produce stresses just under the 

» 

elastic limit. Whatever may have been considered permissible then, 
it is my judgment that the loading should be so modified now as to pro- 
. duce maximum stresses sensibly lower than that limit. It would be 
prudent to limit the greatest possible stresses produced by the “ con¬ 
gested,” dead and wind loads to three-fourths of the elastic limit. 

In view of the increasing concentrated loads of nearly all kinds of 
traffic passing over such a structure as the Blackwell’s Island Bridge, it 
is my judgment that the working tensile stress in subverticals or hangers 
could judiciously be limited to 15,000 lbs. per sq. in. instead of 18,000 
lbs. per sq. in. although the use of the latter value does not prejudice 
the safety or durability of the structure. Such members however are 
subject to shock and greater concentrated loads than may be contem¬ 
plated and a wide margin of safety is advisable for stresses so produced. 

The provisions of the specifications both for the chemical and physi¬ 
cal requirements of the material are in accordance with the best practice 
of the present day and entirely satisfactory. I have as far as possible 
examined the manner of inspection both in the mill and shop, and I have 
scrutinized carefully a mass of records of experimental data established 
by tests of both specimens and full size eye-bars in the course of mill 
inspection with satisfactory results. All of this class of evidence goes 
to show that the material put into the bridge was of excellent quality 
and fully met the requirements of the specifications. 


19 


The character of shop work is evidenced by the condition of the 
manufactured members in the bridge. These are largely open to ocular 
inspection, and I have many times been on the structure for the pur¬ 
pose of examining the results of the shop work. I believe it to be fully 
up to the requirements of the specifications and generally in accordance 
with the best practice of the present time. The four sub-diagonal posts 
C 56-L 57 and L 107-C 108 on both trusses near the main piers on Black¬ 
well’s Island were a little twisted when put in place, but this difficulty 
was corrected by riveting cover plates on the tops of the posts. These 
posts are not main truss members and the question of the safety or 
stability of the latter is in no way affected by them. 

Many sections have been carefully calipered and the weights of many 
members have been computed in order to determine whether the actual di¬ 
mensions of pieces as placed in the structure correspond to the requirements 
of the specifications, contract and shop plans. The results of these examina¬ 
tions have been entirely satisfactory. The actual sections of the members are 
generally found a little full, a margin of 2V2 per cent, being allowed by speci¬ 
fications in accordance with common practice. The total steel in the struc¬ 
ture as built and as determined bv the actual shipping lists and scale 
weights confirmed by the computations mentioned above is shown by the 


following detailed statement: 

Manhattan Anchor Span. 14,501,190 lbs. 

Manhattan Tower . 3 ’ 7 ° 5 > 55 ° lbs. 

Manhattan Cantilever Arm. 13,246,660 lbs. 

Island Cantilever, West. 12,934,040 lbs. 

Island Span . 21,167,080 lbs. 

Island Towers . 6,188,830 lbs. 

Island Cantilever, East. 9,370,900 lbs. 

Queens Cantilever Arm. 9,351,960 lbs. 

Queens Anchor Arm. 11,592,770 lbs. 

Queens Tower . 3,074,800 lbs. 


Total . 105,133,780 lbs. 


I have made a careful examination of the entire structure as far as 
possible, with a view of determining whether evidence of distress of any 














20 


members exist, such as permanent distortion, loose rivets, or other evidences 
of overloading, misfitting or any other circumstance which might indicate 
over-stressing. I have not found such evidence. All parts of the structure 
appear to be in satisfactory condition. There are minor or small varia¬ 
tions from alignment which are usually observed in large completed bridge 
work in place, but nothing whatever to indicate any inherent weakness or 
unsatisfactorv condition. 

In addition to this inspection, I have had accurate surveys made of 
the entire structure to determine the alignment of trusses and elevation of 
lower chord points in July and as late as October 26, the past month. 
These surveys indicate that the alignment of the trusses is entirely satisfac¬ 
tory, and that the deflections vertically are only those caused by the dead 
weight of the structure at the two dates stated, the dead weight at the later 
date being considerably more than at the former in consequence of the 
large amount of floor material put in place within the period named. 

The computations for the stringers and floor beams for both upper 
and lower decks show that in the main, the prescribed unit stresses are 
not exceeded. In a large number, perhaps the majority of cases, the com¬ 
puted stresses are considerably below the specified limits. In a few cases 
of the lower floor beams and trolley stringers, the specified unit stresses 
are to a small extent exceeded. This excess is due to the use of less dead 
load than the weight of the floor as finally constructed. This excess, how¬ 
ever, is too small to be material. 

The outside trolley stringers on the lower floor of the Island span and 
its cantilever arms have been built in accordance with the specifications, 
but while they were being completed, it was thought that the heavier sub¬ 
way cars might at some future time run over these tracks. Consequently, 
the outside trolley stringers on the remainder of the bridge were cover- 
plated to meet the requirements of the increased loading. If, in the future, 
the heavier subway cars should be run over the structure, it would be neces- 
sary, as was intended, to put these cover plates on the stringers of the Island 
span and its cantilever arms, which may be readily done if it should ever 
be required. 

An examination of the design and construction of the anchorages at 
both ends of the structure shows that weights of masonry and other por¬ 
tions of the anchorage and its members are sufficient and satisfactory for 


21 


their purposes. The pressures on the masonry in the main piers are also 
within the requirements of the specifications. 

1 he erection stresses are now of secondary importance, if of any im¬ 
portance at all, as the structure is erected and the erection stresses have 
passed never to recur. These stresses, however, have been computed with 
the weight of the traveller taken at 647 tons distributed as in actual use. 
Two such travellers have been assumed to be in use simultaneously on the 
east and west cantilever arms of the Island span and in positions to pro¬ 
duce the greatest stresses. The results of these computations show that the 
erection stresses in the chords could not at any stage of the construction 
equal those due to the completed dead weight of the structure. In a few 
of the diagonals in the vicinity of the main piers, the erection stresses equal 
those produced by the specified dead and live load. Inasmuch as these 
stresses exist in the structure but once and will never exist again, they have 
no special significance in regard to the carrying capacity of the bridge, nor 
has the weight of the traveller been a test of the structure comparable with 
the traffic loading which must be carried. 

It is to be observed that the specifications do not call for any snow 
loading. In view of the fact that there are occasionally heavy snowfalls at 
New York, sometimes followed by rain and subsequent freezing, it would 
seem to have been advisable to make some suitable provision for this class 
of loading. At the same time, if the usual street cleaning removal of snow 
from the bridge is promptly made, it is clear that there is practically no pos¬ 
sibility of snow load and even the regular live load concurring. The admin¬ 
istration of this structure should, therefore, be stringently carried out to 
meet that requirement, otherwise an objectionable overloading is possible. 

It is assumed throughout this investigation that the adjustment of the 
supports at the ends of the anchor arms is such that the rocker arms are 
subjected to no stress when the bridge is free of live load. The determina¬ 
tion of all stresses requires that condition to be assured after the completion 
of the bridge. 

I have had computed a complete stress sheet for the greatest possible 
stresses in every part or member of the entire structure using the prescribed 
“ congested ” moving load and wind loading and the actual.dead weight of the 
structure as determined by the shipping weight of all the steel and other 
metal members, and by the working plans for the railways, roadways and 


22 


sidewalks of the upper and lower decks. The dead weight of the structure 
thus determined is composed of the items per linear foot of bridge shown 
in detail on the stress sheets. 

The results of these computations show that there are a considerable 
number of the main truss members which would be overstressed under the 
provisions of the specifications for the assumed loading. Some of the bottom 
chord panels of the Island span would carry about 25 per cent, more than 
permitted by the specifications for compression under dead and congested 
live loads. The bottom chords of some other portions of the bridge would 
be overstressed under the same conditions up to a maximum of about 15 
per cent. 

Under the conditions for which this structure is designed, as already 
stated, the top chord and main truss members other than those of the bottom 
chords are not affected by the wind. 

With the same conditions of loading as above, the nickel steel eve-bars 
in the top chords of the Island span would be overstressed about 25 per 
cent, as a maximum, and 20 per cent, in the top chord of the Queens 
cantilever arm, while the maximum overstress in the Manhattan cantilever 
arm and the two Island cantilever arms would be 15 per cent, to 20 per 
cent. The overstresses in a number of the carbon steel eye-bars would 
range from 10 to 15 per cent, in some members in all parts of the struc¬ 
ture except in the Queens anchor arm where 30 per cent, is reached in one 
case. There would be also some similar overstresses in riveted tension 
nrgmber s in the same parts of the bridge rising above 33 per cent, in • 
mmmtm instanced. Few main posts in all the bridge would be overstressed as 
much as 25 per cent. In the Queens anchor arm there is one post which 
would be overstressed 33 per cent. The Manhattan rocker arm would be 
overstressed nearly 20 per cent, in tension and 30 per cent, in compression, 
while the Queens rocker arm would be subjected to an excess of 10 per cent, 
in tension and 12 per cent, in compression. 

Among the secondary or sub-truss members, one hanger near the centre 
of the Manhattan cantilever span would be overstressed about 20 per cent, 
and another about 10 per cent. All other hangers, sub-diagonals and sub¬ 
posts would receive practically their proper stresses only. 

These greatest overstresses running with two or three exceptions not 
above a maximum of 25 per cent, of the stresses permitted under the specifi- 


23 


cations would not be serious if the permitted working stresses were not 
initially high. In fact, there are bridges in use and considered safe in 
which similar overstresses exist although such conditions can never be con¬ 
sidered satisfactory. Again, as none of these excessive stresses per square 
inch of cross-section, even when combined with wind load stresses, exceed 
some of the elastic limits determined by experiment for the corresponding 
members in which they are found, those stresses exceed but little, if any, 
the limits permitted for the stresses due to the congested live, dead and 
wind loads of the Commission of Bridge Experts whose report has already 
been alluded to. In my judgment, however, as already expressed, the maxi¬ 
mum stresses permitted in that report, under the congested, dead and wind 
loads, are too high, and it is further my judgment that these computations 
show that sufficient provision was not made in designing the cross-sections 
of the members of the Blackwell’s Island Bridge for the two additional 
elevated tracks which were added to the structure in 1904. 

It becomes necessary, therefore, to ascertain what is the safe maximum 
loading of this bridge for both the lower deck and the upper deck, includ¬ 
ing in the latter such elevated railway tracks as may be permissible. For 
this purpose it is considered prudent to adopt for the greatest permissible 
working stresses those prescribed in the specifications “ For Dead Load and 
Regular Live Load or for Dead Load and Wind,” except that for reasons 
given later on the working stress for columns will be taken as 20,000-50 i/r. 

Substantial advantage may be gained for the structure by removing 
some portions of the dead load of the floors both for the upper and lower 
decks. An examination of the plans shows that considerable concrete.under 
the two inside trolley tracks of the lower deck as well as some other floor 
details may be either omitted or modified without in any way trenching 
upon the capacity, solidity or strength of the lower floor. Similarly, if the 
two upper elevated railway tracks, including the supporting stringers added 
in 1904, be removed, and if the sidewalk railings of the upper deck be re¬ 
arranged without affecting their capacity or strength, the dead weight of 
the structure may be reduced at least 1,272 pounds per lineal foot of each 
truss on all the cantilever arms. It is conducive to relieving the maximum 
stresses to permit the weight of the lower deck to remain unchanged on the 
Island span and the two anchor arms. The relief of dead weight on those 


24 


three parts of the bridge would then be but 380 pounds per lineal foot of 
truss. 

In considering the maximum loading to be taken in a re-computation 
of stresses, it should be observed that the conditions which will produce a 
congested load in one direction on this or any similar great bridge will be 
likely to stop traffic largely or entirely in the other direction, as has fre¬ 
quently been observed in treatments of this question of congested loading 
for great bridge structures. For this reason, it is believed that 50 pounds 
per square foot of roadway and sidewalk is sufficient for an assumed con¬ 
gested load for the main truss members of the Blackwell’s Island Bridge, 
that loading to cover any or all parts of the structure necessary to give any 
member its greatest possible stress. 

The heaviest trolley car now running in the city with its full load 
weighs 62.000 pounds on four axles, and has an out to out length of 42.5 
ft., thus producing an average load of 1,460 pounds per lineal foot of each 
track. The heaviest motor car running on either elevated or subway track 
when fully loaded has a weight on each of tw r o axles of 30,800 pounds and 
22,200 pounds on each of the other two. As this car has an out to out 
length of 51 ft., its average weight is 2,080 pounds per lineal foot of track. 
The heaviest trailer car now running in the city and fully loaded has a 
weight of 70,000 pounds, with a total length of 51.4 ft., making an average 
load of 1,360 pounds per lineal foot of track. An eight car train composed 
of five motor cars and three trailers giving an average weight of 1,810 
pounds per lineal foot of track will be taken for the moving load on two 
elevated railway tracks of the upper deck. 

All dense trolley or elevated railway traffic on the East River 
bridges of this city must be effectively controlled by proper signals and 
continuous inspection, as experience has demonstrated on the Brooklyn 
and Williamsburg bridges. In computing the stresses in the main truss 
members of the Blackwell’s Island Bridge the same control of the trolley 
traffic will be assumed as that exercised on the Brooklyn Bridge and 
on the Williamsburg Bridge, two succeeding trolley cars being separ¬ 
ated by a clear space of about two car lengths. Similarly, the control of 
the traffic on the two elevated tracks would be secured by making the 
minimum distance between the heads of trains 1,000 ft. as is now done 
on the Brooklyn Bridge. The maximum stresses produced in the trusses 


25 


of the Blackwell’s Island Bridge however are found by placing one 8-car 
train with an average of 1,810 lbs. p. 1. f. of track at the center of each 
of the Manhattan and Queens cantilever spans, making the heads 
of trains about 1,722 ft. apart. Any other arrangement of trains with a 
distance from center to center not less than 1,000 ft. will produce less 
stresses in the truss members than that just described. 

This total moving load representing the maximum permissible traffic 
for the Blackwell’s Island Bridge, arranged with two elevated railway 
tracks and constituting what may be called a congested live load will be 


as follows: 

2 Elevated 8-car trains, at 1,810 lbs. 3,620 lbs. p. 1. f. 

4 Trolley tracks, by 4 by 1,460 lbs. 1,947 lbs. p. 1 . f. 

35.5 ft. Roadway, at 50 lbs. per sq. ft. 1,775 lbs* P- 1 - f* 

22 ft. Sidewalk, at 50 lbs. per sq. ft. 1,100 lbs. p. 1 . f. 


8,442 lbs. p. 1. f. 

This total load of 8,442 lbs. is for each linear foot of bridge covered 
simultaneously by the four classes of traffic, each truss carrying one-half 
of this total. 

The stresses computed for all the main truss members is shown on 
sheet No. 3. The positions of trains required to produce these greatest 
stresses are shown on sheets Nos. 4 and 5. 

Comparing results with the specified permissible unit stresses given 
on page 52 of the specifications and reproduced in the earlier part of this 
report for dead load and regular live load, excepting those for columns 
already alluded to, this stress sheet shows that no unit compressive stress 
in all the trusses exceeds the prescribed working limit. Nor is there 
but one instance where nickel steel eye-bars show stresses as much as 
4 per cent., or, but three instances as much as 3^2 per cent, above pre¬ 
scribed value. Similarly, but one carbon steel tension member shows 
4 y 2 per cent, overstress. These overstresses are too small to be of 
moment and they may be ignored. 

It has been shown by actual computations, therefore, that the Black¬ 
well’s Island Bridge has a safe and satisfactory capacity for carrying 
a volume of traffic under the conditions of control found advisable by 







26 


experience on the Brooklyn and Williamsburgh Bridges, sufficient for 
a considerable future period and perhaps for a long future period. No 
elevated traffic can pass the structure for some time to come as there 
are no connections for such traffic at the Queens end of the bridge. 
Whenever such traffic may be required, the two elevated tracks on the 
upper deck will serve that purpose. The question of further accommo¬ 
dation for lines of traffic on the upper deck may judiciously be left for 
later consideration when demanded by future requirements and when 
the character of traffic to be accommodated at that time shall become 
known. It is only necessary so to adjust the accommodations for such 
future developments as will keep the unit stresses in the main truss 
members within the limits prescribed in the specifications for regular 
live and dead loads or for those loads combined with the wind loading. 

The formula given in the specifications for the safe carrying capacity 
of columns or posts of carbon structural steel members is 20,000-90 1 /r 
lbs. per sq. in. Recent tests of full size members of this class indicate 
deal ly that this formula gives results lower than need be taken for this 
class of members, and hence, in computing the proper working stresses 
for the structural steel members of this bridge, the value 20,000-50 1 /r has 
been used. The ultimate carrying capacity, which is practically the 
elastic limit, of such columns with a ratio of length over radius of gvra- 
tion of 40 to 50 is not less than 31,000 to 32,000 lbs. per sq. in., nor less 
than 28,000 to 29,000 lbs. per sq. in. for a ratio of length over radius of 
gyration of 90. 

I recommena that the Department of Bridges have made and tested 
to destruction not less than six pairs of structural steel compression 
members, each pair being duplicates, similar in cross-section to the 
typical compression members in thq chords and web members of this 
bridge, the areas of cross-section of such columns to be the greatest 
capable of being tested in the testing machines of the largest capacity 
in this country, such test columns to have pin heads. Such tests could 
be made within a comparatively short time; and if the test columns are 
judiciously designed with a range of length over radius of gyration 
varying from 40 to 100, valuable and accurate information as to the 
safe carrying capacity of such members would be disclosed. It is not 
necessary, however desirable it might be, to test columns of the greatest 


27 




area of cross-section in the trusses, which are far beyond the maximum 
capacity of any testing machine now available. 

Approximate computations only have been made for the secondary 
stresses due to the distortion of the trusses by the live load, and by 
the variation of temperature. Although such computations may readily 
be made, it is a matter of grave doubt whether these stresses ever exist 
to the extent indicated by computations. When secondary stresses are 
computed at truss joints, it is essentially impossible to make due allow¬ 
ance for the presence of the heavy joint plates and other details which 
greatly reduce the stresses computed for the sections of the members 
themselves. As a matter of fact, observations on wrecked trusses show 
that in well designed work the joints at which the secondary stresses 
are supposed to be greatest are the parts frequently showing the least 
distress and the greatest rigidity or the least departure from their normal 
condition. The approximate computations made for these secondary 
stresses in a considerable number of truss members show that the com¬ 
puted intensities are below 3,000 to 3,500 lbs. per sq. in. As these maxi¬ 
mum intensities exist in extreme fibres only and probably not to the 
extent shown by the computations, it is clear that they can have no 
material effect upon the safety or stability of the truss members. 

The stresses arising from the bending of horizontal or inclined truss 
members due to their own weight are of a much more definite character. 
Computations of these own weight bending stresses have been made 
on a large number of truss members and they may in some cases run 
as high as 3,000 lbs. per sq. in. to possibly 4,000 lbs. per sq. in., although 
generally of lower value than the former. Again as these are extreme 
fibre stresses only and for short parts of the members in question, they 
may be disregarded as having no material effect upon the proper safe or 
working value of the members in question. 

There are also some stresses which may be called secondary which are 
due to the acceleration and retardation of moving trains upon the elevated 
railway tracks which are supported midway of the vertical web members, 
but they are of such uncertain values, scarcely subject to even approxi¬ 
mate computation, that they may be legitimately considered as incidental 
stresses covered by the margin allowed in determining proper working 





stresses. 


28 


The wind stresses shown on the stress sheet, Sheet No. 3, are compiled 
from the prescribed wind loads and in the manner prescribed by the specifi¬ 
cations. It will be observed that chord stresses only are given as the de¬ 
sign of the bridge trusses with their transverse bracing is such that all 
wind loads are carried down to the lower deck over which a rigid buckle 
plate floor is found. This buckle plate floor and the lower chords constitute 
to a material extent a great plate girder to resist the horizontal wind forces. 
No web stresses are therefore to be determined. As a matter of fact it 
is a question whether even the full computed chord wind stresses can exist. 

Adverse comment has been made on the heavy compression lower 
chords of this bridge and their design therefore has been scrutinized with 
great care. Each chord is composed of two parallel and independent, built- 
up channel compression members connected together with top and bottom 
15-inch by ^-inch batten or tie plates. Each member of this pair of com¬ 
pression chords is composed of two built-up channels with vertical web plates 
48 inches deep and of varying thicknesses to afford the proper area of 
section, each web having 8-inch by 6-inch angles top and bottom. Each of 
these pairs of built-up channels is latticed, top and bottom, with a double 
system of 5-inch by ^-inch lacing bars held by two rivets at each end 
and one at each of the intersections. The entire chord composed of each 
of these two units has therefore a total width of about 82 inches. 

The radius of gyration of each of these chord units about its horizontal 
neutral axis is about 14 inches, while the radius of the same section about 
its vertical neutral axis is about 12 inches. The numerous top and bottom 
batten or tie plates certainly give material horizontal stiffness to the two 
units although not as much as would heavy lattice bracing. It is reasonable 
and safe to give the horizontal radius of gyration of this double column 
section a value of 14 inches identical with that of its vertical radius, and 
this has been done in the computations. It will be found by examination of 
the stress sheet that there are other compression members of the trusses 
which sustain higher unit stresses with a greater ratio of length over radius 
of gyration. There can be no apprehension, therefore, that these lower chord 
compression members are in any way unsafe or of less unit carrying capac¬ 
ity than other main compression members of the trusses. 

No criticism of these lower chord compression members would probably 
have been made except for the failure of chord sections of somewhat similar 


29 


general shape of section in the Quebec Bridge. The similarity, however, 
lies only in the general form of section of the component parts. The spacing 
details of the Blackwell’s Island chord sections, consisting of heavy lattice 
bars, batten and tie plates, and transverse diaphragms, are relatively far 
heavier, stiffer and stronger than corresponding details in the Quebec 
trusses; indeed, in the latter, there were no transverse diaphragms such as 
are found in the Blackwell’s Island Bridge. There is therefore little or no 
similarity as to the unit carrying capacity of the compression chord mem¬ 
bers in the two bridges. 

The deflections of the extremities of the cantilever arms under the 
moving load shown on the stress sheet accompanying this report may be as 
great as 23 inches. In computing this deflection the gross section of 
riveted tension members has been used, and a modulus of elasticity for both 
carbon and nickel steel of 28,000,000 pounds per square inch. This de¬ 
flection would be less if the depth of trusses were greater. Substantial 
economy would have been attained if the trusses had been designed with a 
greater depth and with longer panels in the main truss system, at the same 
time gaining greater stiffness. 

The lateral stiffness of a cantilever structure, especially of this magni¬ 
tude, is of much importance and it is affected greatly by the horizontal 
width between trusses which in the present instance is 60 ft. A comparison 
of the length of the Manhattan cantilever arm, 591 ft., with this 60 ft. 
width between trusses shows that the latter dimension has been judiciously 
chosen, giving to the structure a proper lateral stiffness, especially in con¬ 
nection with the buckle plate floor. 

Conclusions. 

First —The specifications for the chemical and physical requirements 
of both the nickel and carbon steels employed in the structure are satisfac¬ 
tory and in accord with the best practice of the present time. 

$ 

Second —Both the shop and mill inspection were efficiently performed, 
resulting in securing excellent quality of material and the fabrication of 
truss members of good quality and accurate dimensions. 

Third —The various members of the structure possess the full sections 
required by the unit stresses and the working plans, and the shipping 


30 


weights correspond correctly to those sections as well as to the computed 
weights. 

Fourth —The erection was successfully and satisfactorily performed, 
leaving the trusses in correct alignment and elevation. 

Fifth —Computations in accordance with the specifications for the maxi¬ 
mum floor loads show that the capacities of the floors for both the ^upper 
and lower decks are satisfactory. 

Sixth —Computations for all the main truss members of the bridge show 
that the stresses produced by the prescribed congested live load, combined 
with the dead load or with the dead load and wind loading are higher than 
prescribed as permissible in the specifications, and higher than prudent to 
permit, although practically not in excess of the limits approved by the Com¬ 
mission of Expert Engineers in 1903. 

Seventh —The stresses disclosed by the stress sheet submitted with this 
report show that a controlled traffic on the four trolley lines of the lower 
deck and on two elevated railways of the upper deck carrying the heaviest 
cars of their classes now in use in the City of New York together with a 
vehicular traffic on the roadway and two loaded sidewalks may be per¬ 
mitted without exceeding the specified unit stresses for the regular live load 
and dead load and without exceeding the safe limits of stresses for such a 
structure, provided the re-arrangement of the floor of the lower deck and 
the removal of the two elevated railway tracks on the upper deck together 
with the re-arrangement of the sidewalk details be made as indicated in this 
report so as to reduce the dead load by at least 1,272 lbs. p. 1. f. of each 
truss of the cantilever arms and 380 lbs. p. 1 . f. of each truss of the Island 
span and anchor arms. This re-arrangement and reduction of dead load can 
now be made without material delay in the opening of the bridge for traffic. 
The capacity so afforded is satisfactory and sufficient for a considerable fu¬ 
ture period. Any further use of the upper deck for elevated railway or other 
purposes should be deferred until the development of traffic in the future 
may make it necessary, and until it shall be determined what character of 
traffic must then be accommodated, but that adjustment to the future traffic 
should not be such as to produce greater unit stresses than those approved 
in this report. 


3i 


Eighth —The distance between trusses is suitable to this type of struc 
ture and such as to secure satisfactory lateral stability, especially in con 
nection with the buckle plate floor. 

Respectfully submitted, 

Wm. H. Burr, 

Cons. Engr. 


3 2 




APPENDIX I. 

The Cantilever Without Suspended Span. 

A cantilever structure comprising two anchor arms, two cantilever 
spans and an anchor span between the two latter, like the Blackwell’s Island 
Bridge, becomes continuous from anchorage to anchorage when the sus¬ 
pended spans are displaced by rocker arms, vertical in the present case, con¬ 
necting the upper and lower extremities of two adjacent cantilever arms. 
The stresses in the different members of the trusses cannot, therefore, be de¬ 
termined by the ordinary procedures applicable to statically determinate 
structures. It is necessary first to find the stresses (reactions or shears), in 
the rocker arms by the aid of formulae involving the elastic properties of the 
materials of the structure, the latter being loaded in any manner whatever. 
The continuity of the trusses makes it necessary to recognize, in the analysis, 
the simultaneous existence of the two rocker arm reactions or shears. 

The complete determination of the general values of those reactions or 
shears is as follows. 

The Two Reactions or Shears Rl and Fj. 



To make the case general it will be assumed that the lengths of canti¬ 
lever arms on the right and left, respectively, are unequal and represented 
by / R and / L . The length of the rocker arm CB is h, and its area of 
cross section A. The line LR in Fig. 2 is supposed to represent the lines of 











33 


the cantilever arms, at the same elevation, before the structure is so loaded 
as to cause unequal deflections. 


L 


n 



Fig. 2. 


The principal quantity to be found is the force or reaction exerted be¬ 
tween the ends of the cantilevers through the rocker arm BC and when 
loaded in any arbitrary manner. All other desired quantities can then be at 
once determined. 

If all connection between the extremities of the cantilever arms is cut 
when those arms are loaded in any arbitrary manner, in general the end 
of the right arm will have the deflection a r while the deflection of the 
left end will be a l - If, on the other hand, the ends are connected by 
an elastic member they will deflect to some points G and K between the 
lower limits of a r and a l . Let the force or reaction exerted in this 
elastic connection be represented by R*. Also in Fig. 2 let a r represent 
HK while a r represents JG, remembering that HK and JG are the 
downward and upward deflections produced by the force or reaction R* 
acting at the end of each cantilever arm as if the latter were free of any 
end connection. Then let <*> be any arbitrary load supposed to act at the 
extremity of each free cantilever arm and to produce there the deflections 
5 r and S L in the right and left arms respectively. Since these de¬ 
flections are proportional to the forces producing them: 



1 









34 


K h 

EA 


The change of length of the rocker arm CB caused by the stress in it is: 
• E being the coefficient of elasticity. 


In this analysis downward deflection will be considered positive and 
upward deflection negative. In the case of Fig. 2 a£ would be negative. 


Furthermore: aJ-Al = a l 


a r — 


K h 

EA 


2 


Substituting for Ar and a[ from Eq. 1 in Eq. 2; 

( A l Ar)® 




d R — 


I + 


GO 


EA(Sr -s l ) 


If Fig. 2 be supposed applied to span l', a r will be of Eq. 3, 
while Aj will be a r of that equation in consequence of the sym¬ 
metry of arrangement of spans / 2 , / and /. 

If the division indicated in the bracket of the second member of Eq. 3, 
be carried out for two terms only, there may be written approximately: 

( A l — A r) go I 


K = 




h GO 

L 1 “ EA(6r- 5 l) J 


There is no special advantage in the form of Eq. 4. Equation 3 was 
used in all the computations covered by this report. 

The fraction whose numerator is h go in the bracket of ihe second 
members of Eqs. 3 and 4 is the allowance or correction to be made in the 
value of the reaction IT for the extension or compression of the rocker 
arm, and it may be omitted if that member is very short and of large cross 
sectional area. 


SPECIAL VALUES OF REACTION R\- 

For the purposes of this analysis an upward reaction will be consid¬ 
ered negative and a downward reaction positive. 

N 

If the load producing R* is wholly on the left cantilever arm, so 
that a r = o, a l only existing, Eq. 3 at once gives; 

a l ® 


r i-« r -5 


1 + 


GO 


EA (*r-« l ) 


5 




















35 


On the other hand, when the right arm is loaded so that 
only existing, Eq. 3 will give: 


= o. 


R 




‘ R 


GO 


R 


I + 


h GO 


EA (d R #l) 

It is thus disclosed that the general value of the reaction R* is the 
algebraic sum of the two special reactions. Hence, if a certain loading 
produces a special reaction R* and another loading the special reaction 
R^, each causing a corresponding set of stresses in each arm, the result¬ 
ant reaction caused by the concurrent action of the two loadings will be 
the sum of the two special reactions and the stresses produced in the vari¬ 
ous truss members will be the algebraic sum of the stresses corresponding 
to those two special reactions. 


APPLICATION TO BLACKWELL’S ISLAND BRIDGE. 

All the preceding formulae are perfectly general and applicable to 
any number of spans. In applying them to any special case, as that indi¬ 
cated by Lig. 3, due regard must be shown to the values and signs which a l 
and a r will then take. This may be illustrated by considering the par¬ 
ticular structure shown by Lig. 3. There can be no shear or reaction R* 
in the span / ? Lig. 3, without a corresponding shear or reaction R* in 
the span /; and the same observation is to be made regarding the de¬ 
flections at those two points. 

If d 2 is the deflection at C, Lig. 3, due to any arbitrary load, 

(as 1 or 1000 pounds) acting at D in l', then the deflection at the same 
point C due to the shear or reaction R* at D, expressed in the same 

unit go, will be: R* 

d —A 

GO 


m 2 m 3 



Hence in Eq. 3, there must be written for a r the two terms 

d T5 I 

a r + 2 4 ; a r now representing the deflection of the extremity of the 




GO 




























3 ^ 


cantilever CM 2 due to any loads resting upon the structure between C 
and D. Similarly if d 4 represents the deflection of the extremity of the 
cantilever DM 3 due to the action of the same arbitrary load or unit at C, in 
the value of Rh* 

4 

r go 

r 1 _ ( A R a l ) h go .. y 

4 d L d R 1 + EA (^ L — Sr) 

R 1 d 

there must be written a l + 2 4 for a l f n Eq. 7; a l now represent¬ 
ed 

ing deflection due to load on CD. 


There may then be written the following two equations by the aid of 
Eqs. 3 and 7. 



It must be carefully borne in mind that the same letter in the two 
equations 8 and 9 does not in general possess the same numerical value for 
any given structure, although in most cases h and A may have the same 
values. 


Let there be placed in Eq. 8: 


2 . ts x \ 1 h go 

( 5r L)+ EA 

Also, in Eq. 9: 


4 = 


GO 


Sr — S 


r) T 


h GO 

TAT 



11 


Then: 



a \ a 2 d 2 R I 

a r) 2 -^ 7 T J 

GO 


12 




a 4 d 4 R 2 


GO 


13 

































37 


Eliminating between Eqs. 12 and 13: 


*; = a 2 


( A ..- a r ) 2 + ^t( a l 

~ -vr 

1 — a a _ 2 — 4 

2 4 2 

GO 


a r ) 4 


d 


R 5 = - 3 4 


Ol - a r ) 4 + ~ 77“ 4 ( A 


A 


R /2 


d 2 d 4 
*-*2 a 4 ~^ 
GO 


14 


15 


The subscripts 2 and 4 affecting the parentheses in the numerators of 
the second members of Eqs. 14 and 15 indicate that the quantities ( a l ~ a r) 
belong to the spans / 2 and / respectively. 

Eqs. 14 and 15 give the two shears or reactions R 2 and Rj at the 

• * 

extremities of the cantilever arms. When these two reactions are deter¬ 
mined, the ordinary analytic or graphic methods for determining the stresses 
in all members of the entire structure from anchorage to anchorage may 
be applied. These operations were followed in computing the stresses 
shown on the sheets accompanying this report. 

It will be observed that in Eqs. 14 and 15 the only variable quantities 
are a r and a l which are to be found by the aid of stresses determined 
by ordinary statical methods. 

Wm. H. Burr, 
Cons. Engr. 











Alfred P. Boller. 
Henry W. Hodge. 


Telephone, 94 Rector. 
Cable Address, “ Bolodge.” 


Boller & Hodge, 

Consulting Engineers, 

1 Nassau Street, 

New York. 

New -York, October 28, 1908. 

Hon. Jas. W. Stevenson, 

Commissioner of Bridges, 

City of New York: 

Dear Sir —In accordance with the resolutions of the Board of Esti¬ 
mate and Apportionment, dated June 5th, and your instructions of June 9, 
% 

1908, we have made a careful investigation of the carrying capacity of the 
Blackwell’s Island Bridge over the East River, and hand you herewith a full 
report of the results of this investigation, accompanied by ten drawings, and 
one appendix. 

We beg to say that your Department has put all the records and data 
of this entire structure at our disposal, and has extended every assistance 
and courtesy in aiding us to arrive at the necessary facts on which our in¬ 
vestigation is based. 

Yours very truly, 

Boller & Hodge, 

Cons. Eng’rs. 


H. W. H. 


39 


Boller & Hodge, 

Consulting Engineers, 
i Nassau Street, 

New York. 

Report on the Carrying Capacity of the Blackwell’s Island Bridge. 

The Blackwell’s Island Bridge in New York City, across the East River, 
extends from Sixtieth Street and Second Avenue, Borough of Manhattan, 
to Jackson Avenue and Jane Street, Borough of Queens, a distance of about 
8,600 feet, made up of steel viaduct approaches at each end with a canti¬ 
lever structure over the two channels and over Blackwell’s Island, having a 
length of 3,724^ feet between anchorages, with spans as shown on Diagram 
No. 1. 




















































































































I 






































43 



1 lus CciiitilcA ci stiucture differs from the usual type in having' the lower 
ends of each shore lever arm attached by a rocker arm to the upper ends of 
each Island lever arm, thus making the entire structure continuous. 

In accordance with our instructions we have confined our investigation 
to the cantilever structure, and all of our findings apply only to that portion 
of the bridge between the anchor piers. 

This cantilever was originally designed to carry a 35^-ft. driveway, 
two 11-ft. sidewalks, four lines of trolley cars and two lines of elevated rail¬ 
way, arranged as shown on Diagram No. 2. 

Diagram No. 2. 


1 • 

u- & -*j 

* I 

CROSS SECTION. 

The contract for this structure was let to the Pennsylvania Steel Co. 
on November 20, 1903, and this contract design as shown by the lithographed 
album of drawings, together with the printed specifications issued with this 
album of drawings, will hereafter be referred to as the original design. It 
was estimated that the weight of the original design would be 84,300,000 lbs., 
made up as follows: 

Nickel steel eye-bars .. 12,200,000 lbs. 

Nickel steel pins . 1,100,000 lbs. 





























































































44 


Structural steel eye-bars . 400,000 lbs. 

Structural steel pins. 50,000 lbs. 

Structural steel, other than eye-bars and pins. 69,550.000 lbs. 

Steel castings . 1,000,000 lbs. 


84,300,000 lbs. 

But the final sections and details had not been made when this estimate 

% 

of weight was given, so the full data for an accurate estimate of weight did 
not then exist. 

In September, 1904, it was decided to add two more lines of elevated 
railway to the original design, and these were to be arranged as shown 
on Diagram No. 3, the sidewalks being placed outside of the trusses. 


Diagram No. 3. 



CROSS SECTION. 


\ 


But it was determined that the four elevated tracks would not be im¬ 
mediately needed, so the bridge is now built with the outside footwalk 
stringers and the overhanging ends of the upper floor beams omitted, with 
















































































45 


the sidewalks placed (for the present) in the place of the tw<p outside ele¬ 
vated tracks, as shown on Diagram No. 4. 


Diagram No. 4. 



The original specifications called for a “ congested ” live load of 12,600 


pounds p. 1. f. bridge, made up as follows: 

2 Elevated Railway Tracks at 1,700 lbs. p. 1 . f. = 3,400 lbs. p. 1 . f. 

4 Trolley Railway Tracks at 1,000 lbs. p. 1 . f. = 4,000 lbs. p. 1 . f. 

35^-ft. roadway at 100 lbs. per sq. ft. = 3,550 lbs. p. 1. f. 

2 11-ft. sidewalks at 75 lbs. per sq. ft. = 1,650 lbs. p. 1. f. 


12,600 lbs. p. 1. f. 

and a “ regular ” live load of one-half the amount or 6,300 lbs. p. 1 . f. 

But when adding the two additional lines of elevated railway these 
loads were increased by the weight of these two additional tracks, giving a 
“ congested ” live load of 16,000 lbs. p. 1. f. bridge, and a “ regular ” load of 
8,000 lbs. p. 1. f. bridge. 


\ 








































































































46 


These uniform loads were specified for the main truss members only, 
and the floor systems and secondary truss members were to be designed for 
the following live loads : 

On each elevated railroad track r - 4 - * - 4 : /o' (f) 6 (f) 

2&obo zeooo " 2tooo i\ooo 


On each street car track 


4 

ovc 


26000 


/o ‘ O _or 1800 lbs. per lin. ft. of track. 

26000 


On any part of the roadway 48000 lbs. on two 
axles 10 ' apart and 5 ' gauge covering a space 
12 'x 30 ', and 100 lbs. per sq. ft. on the 
remaining roadway surface. 

On the footwalk a load of 100 lbs. per sq. ft. 


/to> 

13 - / 0 ' 7 Io 

Qo 

/2C 

J ^ 

• 

a 3 

V 

Too /£ 

000 


jo 


T 

• , 
/2 

1 


The dead weight was specified to be the weight of the structure and 
floor, without any allowance for snow. 

The wind load was specified to be 2,000 lbs. p. 1 . f. bridge, of which 
1,000 lbs. was assumed to be a moving load and 1,000 lbs. a fixed load. 

The specifications state that some of the eye bars and pins will be of 
nickel steel of the following chemical requirements: 

Per Cent., Max. 


Phosphorus (Basic) ...04 

Phosphorus (Acid) .06 

Sulphur .05 


Per Cent., Min. 

Nickel.^. 3.25 

The annealed specimens of this material were required to have the fol¬ 
lowing physical values: 

Elastic limit. 48,000 lbs. minimum per sq. in. 

Ultimate strength. 85,000 lbs. minimum per sq. in. 

1,600,000 


Elongation in 8 inches 


ultimate. 


The full sized annealed bars of this material (up to a maximum size of 
16 inches bv 2^ inches) were required to show the following results: 

Elastic limit. 48,000 lbs. minimum per sq. in. . 

Ultimate strength. . . .'. 85,000 lbs. minimum per sq. in. 

Elongation in 18 ft. 9 per cent. 




























47 


All other material in the structure was to be of open hearth steel, speci¬ 
mens (except rivets and steel casting’s) to show the following chemical 
results: 

Per Cent., Max. 


Phosphorus (Basic).04 

Phosphorus (Acid).08 

Sulphur .05 


And to have the following physical values: 

Elastic limit, plates and shapes. . . . 30,000 lbs. per sq. in. minimum. 

Elastic limit, eye bars. y 2 of ultimate. 

Ultimate strength, plates and shapes 60,000 lbs. desired. 

Ultimate strength, eye bars. 66,000 lbs. desired. 

Elongation, per cent, in 8 inches. . . —r-r— I - ^ Q ° - QQC) -— 

ultimate strength. 


And annealed full-size eye 1 }ars to show results as follows: 

Elastic limit . 28,000 lbs. per sq. in. minimum. 

Ultimate strength. 56,000 lbs. per sq. in. minimum. 

Elongation in body of bar. 10 per cent. 

We have examined the detailed reports of the mill inspectors on this 
material, and find that they show the metal fulfilled the above specifications. 











48 


With the above loads and quality of material, the following unit 
stresses were specified: 


For Dead 
Load and 
Regular Live 
Load or for Dead 
Load and Wind. 


For Dead 
Load and 
Congested 
Live Load. 


r 


For Nickel Steel in Eye Bars and Pins: 

Tension . 

% 

Shear on pins. 

Bearing on diameter of pins. 

Bending on outer fibre of pins. 


Pounds Per Square Inch. 


30,000 

39,000 

20,000 

24,000 

40,000 

48,000 

40,000 

48,000 


For Structural Steel in Main Members 
of Trusses, Towers and Bracing: 

Tension . 

Compression . 

Shear on shop rivets, bolts and pins. 
Bearing on diameter of shop rivets, 

bolts and pins...-. 

Bending on outer fibre of pins. 


20,000 

20,000-90 1 /r* 
13,000 

25,000 

25,000 


24,000 

24,000-100 1 /r 
16,000 

30,000 

30,000 


For Structural Steel in Secondary 
Members of Trusses: 

Tension in sub-verticals (hangers) . . 

Compression in sub-diagonals. 

Shear on shop rivets and bolts. 

Bearing on diameter of shop rivets 
and bolts . 


Pounds Per Square Inch. 


18,000 

18,000-80 i/r* 
12,000 

24,000 


For Structural Steel in Floor System 
of Roadway and Footways and in 
all Floor Beams: 

Tension chords . 15,000 

Shear on shop rivets, bolts and web- 

plates, net section. 10,000 

Bearing on shop rivets and bolts. .. . 20,000 


* Where i=length and r=radius of gyration both in inches. 


















49 


For Dead 
Load and 
Congested 
Live Load. 

f ---> 

Pounds Per Square Inch. 


For Structural Steel in Floor System 
(Including Brackets) for Railroad 
and Trolley Tracks: 

Tension chords . 10,000 

Shear on shop rivets, bolts and web- 

plates, net section. .. 7,000 

Bearing on shop rivets and bolts. . . . 14,000 

Allowable Pressure on Masonry: 

For dead load and regular live load. . 550 

For dead load and congested live load 650 


These specifications and original contract drawings, which show 
the general dimensions of the bridge as built, form the basis of our 
investigation, and in addition thereto we used the detailed shipping 
invoices showing the exact scale weight of each and every piece in the 
structure, and the detailed shop drawings showing the areas of the 
sections. 

We also computed, from the various contract drawings, the weight 
of the flooring material, including paving blocks, roadway concrete, side¬ 
walk concrete, rails, ties and other materials for the various tracks, rail¬ 
ings, pipes, wires and all other material required on the structure. 


For Dead 
Load and 
Regular Live 
Load or for Dead 
Load and Wind. 






50 


We also figured the amount of steel which will be required at some 
future time to complete the two sidewalks in their final position (as 
shown on Diagram 3) and all of these weights were found to be as 
follows: 

lbs. p. 1. f. lbs. p. h f 

bridge. bridge. 


2 outside footwalk stringers. 176^ 

Overhanging footwalk brackets. iooJAdd'l steel.... 

Footw^alk gratings. 127J 

2 upper outside railings. 142] 

2 upper inside railings. 90C. 


Reinforced concrete slabs for footwalk. 

Rails and contact rails for four upper tracks 
Guard timbers and ties for four upper tracks 


403 


232 

=:oo 

330 

640 


2 lower railings. 174 

Rails and conductor rails, 4 lower tracks. ... 375 

Wood paving blocks of roadway.1,041 

Concrete under roadway paving blocks.3,200 

Pipes, mail chutes, telephone, telegraph and feeder wires. 405 - 


7,300 

This total load of 7,300 lbs. p. 1 . f. bridge is referred to in this report 
and on the drawings as “ additional material ” being all the dead load 
except the shipped weight of structural steel. 

From the above data we have carefully computed the live and dead 
stresses and unit stresses in each and every fnember of the structure, 
making our calculations on the following basis: 

Dead Load. —We have taken for the dead load the scale weights 
of each piece as shipped and given on the various invoices, and we have 
apportioned these shipping weights to their proper panel points, arriv¬ 
ing at the panel point dead loads as shown in detail on sheets 1 to 3, 
inclusive. To these scale weights of structural material, we have added 
the weight of “ additional material " as heretofore given ; this material 
being taken as uniform along the entire length of bridge, and apportioned 
to the panel points in proportion to the panel lengths. These two items 
constitute the entire dead load of the completed structure, and the result- 


/ 

















5i 


ing panel loads aie shown in detail on sheets i to 3 and are summarized 
on sheets 4 to 6, which latter sheets show the points of application as 
used for the dead load calculations. 


d he actual shipping weight of steel now in the structure, as at 
present finished (as shown on Diagram 4) is 105,152,010 lbs., made up 


as follows: 

Nickel steel eye bars. 9,179,133 lbs. 

Nickel steel pins . 1,460,563 lbs. 

Nickel steel links and pin plates. 1,010,034 lbs. 

Nickel steel castings . 119,900 lbs. 


Total nickel steel. 

Structural steel eye bars . 5,654,400 lbs. 

Structural steel pins. 38,566 lbs. 

Structural steel other than eye bars 

and pins . 84,795,779 lbs. 

Steel castings . 2,253,094 lbs. 

Small iron castings . 47,786 lbs. 

Cast-iron curb. 592,755 lbs. 


11,769,630 lbs. 


Total structural steel 


93,382,380 lbs. 


Total weight. 105,152,010 lbs. 

This weight is distributed as follows: 

Towers . 12,633,200 lbs. 

Anchorages . 995.500 lbs. 

Trusses, Bracing and Floor. 91,493,310 lbs. 


Total . 105,152,010 lbs. 

The dead load® stresses have been figured on the assumption that 
both rocker arms will be adjusted when the entire dead load is in place, 
so that no dead load will pass through them, thus making the dead load 
stresses entirely independent of these rocker arms and making their 
values computable by the ordinary static methods. 

Live Load.— In accordance with the terms of the specifications, we 
have assumed the live load to be “ placed so as to give the greatest strain 
























52 


in each part of the structure,” and this condition requires that some sec¬ 
tions of the bridge may be loaded and at same time other sections un¬ 
loaded ; for instance, the maximum compression in the rocker arms 
occurs with the two Island lever arms, and the two shore anchor arms 
loaded, and the other portions unloaded, and the maximum tension in 
these rocker arms occurs with the two shore lever arms and the Island 
span loaded and the other portions unloaded. 

For the secondary members, except in a few cases where the bottom 
chord is not straight between adjacent main panel points, the live load 
stresses were figured with the local loads specified. 

As the two rocker members connecting the ends of the lever arms 
cause the adjacent ends of the lever arms to move up and down together, 
the structure is continuous from end to end for live load stresses, and 
these stresses cannot be computed by the usual static method and must 
be found by means of the elastic properties of the materials. 

% 

While this method is well known and has been in use for some time, 
we give in an appendix an adaptation of it to this structure, which takes 
into account the simultaneous action of both the rocker arms and gives 
a simple and precise method of computing their stresses for any given 
loading. 

This adaptation has been worked out by Mr. Clarence W. Hudson, 
who has had charge of these calculations for us. 

With the stresses in the rocker arms known, the stresses in all 
the other members of the structure may be readily computed. 

In computing the deflections of this structure, we have used the 
gross area of all riveted tension members. We have allowed nothing 
for play of pin holes, and we have not considered the tie plates, battens, 
or lattice on riveted members, nor the influence of the lateral system or 
the buckle plate floor. All of these matters have some slight influence 
on the actual deflections, but as it is only the ratio of certain deflections 
that is used to determine the stresses, to a certain extent, one influence 
ofifsets the other, and the stresses thus determined are not subject to 
serious error. We have computed deflections, using a modulus of elas¬ 
ticity of 28,000,000 lbs. for both carbon and nickel steel. 

Wind Loads. —We have computed the wind stresses on the assump¬ 
tion that all wind pressure is transmitted by 'the transverse bracing 


\ 


53 

directly to the lower chord, the upper horizontal bracing being for 
vibration only. 

We have computed the stresses for a fixed load of 1,000 lbs. p.l.f. over 
the entire structure and for an additional live load of 1,000 lbs. p.l.f. placed 
so as to give the greatest stress in each member. 

The wind stresses have been computed by the same general method 
that was used for the live load stresses in the main trusses. 

The formulae for these wind stresses are similar in terms to those for 
the live load stresses, but differ in some of their signs due to the fact that 
a horizontal force at one end of either of the Island lever arms produces 
motion at the end of the other lever arm opposite in direction to the force. 

We only show the chord stresses on our stress sheet as the web stresses 
cannot be given with accuracy since there is a solid buckle plate floor which 
carries a large portion of the wind shear. 

Erection Stresses —We have computed the erection stresses using a 
traveller weighing 647 tons distributed as shown on sheet 10. This weight 
and spacing we have taken from the contractor’s drawings (as this traveller 
had been removed before we started this investigation). 

For the stresses in the Island span we have assumed a traveller on 
the East and West lever arm simultaneously, and we have taken traveller 
weights in such positions as to give maximum strains in every member, 
with the outer limiting position of the forward wheels 4 panels from the 
ends of the lever arms. 

I11 addition to the stresses caused by the travellers, we have computed 
the simultaneous dead load stresses, assuming that all the weight of steel 
was in place, but not including the weight of “ additional material ” 
(amounting to 7,300 lbs. p.l.f. bridge), none of which was placed on the 
structure until after the removal of the travellers. 

All erection stresses have been computed by simple static methods as 
the rocker arms were not rigidly connected till after the removal of the 
travellers. 

Snow Load —The specifications do not call for any snow load on this 
structure, so that we have not figured any stresses for such a load, but in 
our opinion, a bridge of this character, with a practically solid lower floor 
87 feet wide and an upper deck with two sidewalks and four lines of rail¬ 
road track, should have been calculated for a considerable snow load. 


54 


We made a stress sheet for the loads called for in the specifications, 
but it was evident that the structure could not safely carry these loads, 
so we had to find the maximum safe carrying capacity of the structure. 
The final stresses under the conditions of safety hereinafter recommended 
are shown on our general stress sheet (Sheet No. 7) submitted herewith. 
This stress sheet also shows the effective area of each member, the final 
unit stresses, and the wind stresses in the chords. 

The areas marked T for the main posts, U17-L17, U57-L57, U75-L75, 
and U107-L107, are the areas at their points of maximum width, and these 
posts decrease in area towards their ends, as the side plates keep the same 
thickness but decrease in width, giving the areas marked B at the bottom. 
The areas marked T for the other vertical posts are exclusive of the area 
of the transverse diaphragms in these posts, and the areas marked B are 
inclusive of these diaphragms. 

We have made no additions, for reverse stresses, as the specifications 
state that the sections are to be computed for the stress requiring the great¬ 
est area, so that the unit stresses here shown are the direct stresses from 
dead and live loads without any additions for reverse stresses, snow, wind, 
impact, or secondary stresses. 


We have also computed the stresses in many of the floor beams and 
stringers for the upper and lower floors, using the local live loads speci¬ 
fied, and for the cases computed we find the maximum flange stresses to be 
as follows: 

Lower floor trolley stringers with 

cover plates . from 4,600 lbs. to 7,000 lbs. per sq. in. 

Lower floor trolley stringers with¬ 
out cover plates. from 7,200 lbs. to 11,000 lbs. per sq. in. 

Lower floor roadway stringers. . . from 7,900 lbs. to 14,600 lbs. per sq. in. 

Upper floor elevated railway 

stringers . from 6,500 lbs. to 9,100 lbs. per sq. in. 

Upper floor sidewalk stringers. . . from 4,100 lbs. to 10,800 lbs. per sq. in. 

Upper floor floorbeams. from 13,000 lbs. to 14,400 lbs. per sq. in. 

Lower floor floorbeams. from 15,000 lbs. to 16,000 lbs. per sq. in. 

All of these stresses are for the static loads without impact. 

The two pairs of outside trolley stringers on the lower floor are built of 
certain sections on the Island span and its lever arms, and of the same sec- 







55 


tions (for similar panel lengths), with additional cover plates on all other 

* 

portions of the structure, thus making some portions of these tracks much 
stronger than others, as shown by the above stresses. 

We are informed that the Island span and lever arm outside stringers 
had been completed for the specified trolley loads, when it was decided that 
subway trains might be run on these tracks and the remaining outside 
stringers were cover-plated. This, however, leaves these tracks without 
uniformity as to carrying capacity, unless cover plates are added to the out¬ 
side stringers on the Island span and its lever arms. 

The upper floor beams all have the same thickness of web, and the first 
cover runs the full length top and bottom, regardless of whether they carry 
a 20^-ft. panel or a 40-ft. panel, and this was undoubtedly done to carry the 
traveller during erection. 

In a few of the lower floor beams and trolley stringers, the unit stresses 
exceed those specified; and this excess has been caused by their having been 
computed for a dead load less than the actual weight as finally called for 
by the flooring contracts, but this excess is so slight that, in our opinion, it 
will not affect their safety. 

While the erection stresses are passed and can never recur again, we 
considered it advisable to compute these stresses to find if they had been 
greater than the stresses to which the structure may be subjected under 
traffic; and on sheet 10 we give the erection stresses for the chords and for 
such web members as will have the maximum erection stresses, though we 
did not consider it of sufficient value to compute all the minor web stresses 
from erection. 

From this stress sheet we find that the maximum erection stresses in 
the chords do not equal the completed dead load stresses, and only in a few 
diagonals near the main piers do they equal the specified live and dead load 
stresses; so they furnish no data in the way of a full size test to determine 
the carrying capacity of the members, as the structure under tiaffic will be 
subjected to greater stresses than it was during erection. 

We have examined the general design and details of the anchorages 
at the Manhattan and Queens ends and find the sections and the weight of 
masonry sufficient to carry the uplifts. We also find the pressure on the 
masonry of the main piers to be within safe limits. 


5 & 


We have not made a complete investigation of the secondary stresses 
in this structure, but we have made a limited investigation to approximately 
determine what the secondary stresses caused by temperature, distortion 
due to deflection, and bending due to own weight of members, amount to. 

We find that the secondary stresses due to temperature are generally 
small, except in the post U75-L75, where in our opinion, the maximum stress 
from this source will occur, as this is the free end of the Island span, and 
a variation of ±60° F. will move the top of this post and bend it around 
its fixed lower end, producing a fibre stress of 3,200 lbs. per sq. in. 

The secondary stresses, due to distortion of the true figure of the trusses 
by the live load, are quite considerable, as the vertical deflection of the point 
L37 is 18 5/10 inches, and of the point L91, 14 2/10 inches for a live load 
of 3,000 lbs. p. 1. f. truss. 

We have made a careful analytical computation of the horizontal move¬ 
ment of the point U17 (and ether similar points over the main piers) caused 
by this distortion, and for a live load of 3,000 lbs. p. 1. f. truss in the position 
giving the maximum direct stress in the post U17-L17 we find this move¬ 
ment causes a fibre stress in the lower fixed end of U17-L17 of 2,600 lbs. 
per sq. inch, which is the maximum stress from this source, which occurs 
simultaneously with a maximum direct stress. The fibre stresses in the 
other similar posts are about the same, except that for U75-L75 it is reduced 
to 1,400 lbs. per sq. inch owing to the fact that this is the free end of the 
Island span; but this should be added to the temperature fibre stress in this 
post as above given. This distortion also causes some horizontal movement 
of the top ends of the rocker arms relative to their bottom ends and this 
relative movement causes additional secondary stresses, but the stresses 
found from this cause were so small as to be safely negligible. 

The fibre stresses due to bending of members from their own weight 
depends to some extent on the total live load and dead load direct stresses 
on the members, but for a live load of 3,000 lbs. p. 1. f. truss we find this 
fibre stress to be about 1,200 lbs. per sq. in. for many of the members, with 
extreme values running as high as 3,500 lbs. per sq. in. 

There are also secondary stresses due to impact, and to bending in the 
vertical posts and hangers, caused by accelerating or retarding the moving 
loads on the upper floor, but we have not computed any values for these, 


57 


3 .s \\ e arc of the opinion that they are negligible in this structure where the 
relative value of live load as compared with the dead load is so small. 

The above maximum values of all these secondary stresses will prob¬ 
ably not occur in the same members at the same time, but it will be seen that 
they may cause considerable increases in the direct unit stresses heretofore 
shown. 

In addition to figuring the stresses on all members we have had a large 
number of the actual bridge members measured and calipered in the field, 
and we find that they agree with the sections we took from the shop draw¬ 
ings and used in these calculations, which sections we show in detail on 
sheets 8 and 9. 

We have also computed the weight of a number of members from the 
shop drawings and find such weights agree with the shipping weights on 
the invoices, showing that the scale weights used for the dead load are 
correct. 

We have figured the net sections of the riveted tension members from 
the shop detail drawings. 

We have not carefully examined all the details of this structure, but we 
have checked the end connections of such members as are most heavily 
stressed and find them equal in strength to those members. 

> 

We have carefully considered the form and details of the lower chord 
as this feature has been criticised in the public journals, and the impression 
has been given that the lower chords in this structure are weaker than those 
of the Quebec Bridge, which, in our opinion, is not the case. 

There is no full-size experimental data for the carrying capacity of 
such large compression members as are used in this structure, though the 
recent tests on models of compression members for the Quebec Bridge 
showed that such members when properly latticed carried 32,000 lbs. per sq. 
in. before failure, with a ratio of length to radius of gyration of 25. The 
only safety is to keep within the limits gained from experience on a smaller 
scale, as the means do not exist for learning the absolute carrying capacity 
of such sections, and a practical method of testing could not be provided 
in any reasonable time. 

In our opinion, however, it is safe to follow the established practice for 
compression values, provided the limits set are not too high and the details 
are sufficient to make the member act as a unit and not fail in detail. 


58 


The heavier sections of the lower chord of this bridge are built up of four 
vertical webs, each 48 inches deep and varying in thickness with the sections 
required. Each web has an 8-inch by 6-inch angle, top and bottom, forming 
a “ built-up channel.” Each outside pair of these “ built-up " channels is 
latticed together, top and bottom, with 5-inch by 5^-inch double lacing bars, 
having two rivets in each end and one rivet at each intersection, the length 
of these lattice bars being about 45 inches, c. to c. of end rivets. This gives 
two separate built-up channel chords 48 inches deep and 25 inches b. to b. 
of angles. These two separate sections are then connected together 
with top and bottom tie plates 15 inches long and ^2 inch thick, spaced 
about 5 feet, c. to c. The entire chord is thus about 70 inches wide, b. to 
b. of outside angles. While this chord is not as stiff transversely as it would 
be if properly latticed from outside rib to outside rib, and while in our 
opinion the lattice on the centre line, where the longitudinal shear due to 
bending is at its maximum, should not have been omitted, yet we believe 
that the chord is as strong horizontally as vertically for the following 
reasons: 

The radius of gyration of the chord about its horizontal axis averages 
14 inches and the radius of gyration of each outside latticed pair of chan¬ 
nels around a vertical axis averages 12 inches, without any allowance for 
the connecting of these two pairs by the tie plates, which certainly add ap¬ 
preciably to the transverse stiffness, though the exact amount cannot be 
computed. However, the radius of gyration of the whole chord as a unit 
around a vertical axis is about 27, and while it would not be safe or proper 
to use this radius (owing to the omission of <the central latticing), we 
consider it safe to assume that the tie plates add sufficient stiffness to in¬ 
crease the effective radius of gyration about a vertical axis from 12 to 14 
and thus equal the vertical stiffness which of course sets the limit of stiff¬ 
ness for the section. 

We have used for this chord a radius of gyration of 14, and all our 
results are based on this radius, and we are of the opinion that the details 
are sufficient to cause it to act as a unit with this radius. 

The stress sheet shows that there are other compression members in 
the web system of the trusses which have higher unit stresses than the lower 


59 


chord, with a greater value of L/R, so the safety of the bridge is not alone 
determined by the value of this chord. 

We have made a careful examination of the bridge as now completed, 
and find no evidence of loose rivets or buckling of members, or other indi¬ 
cations of overloading, but there are four sub-diagonal posts C56-L57 on 
both trusses, and L107-C108 on both trusses, which had a “ wind ” in them 
during erection, and this was corrected by riveting a cover plate on the top 
of each post. 

It will be noticed that both of these members are “ sub-diagonals ” 
which in no way affect the main stresses and are only for the support of one 
local panel load, and the stress sheet shows that they will never be subject 
to heavy stresses, so they are evidently safe and the “ wind ” was probably 
due to a bend in the shop or during erection, or to a slight over-run in 
length. 

From the above data we come to the following 

Conclusions : 

First —That the specifications are clear and explicit and cover ail the 
necessary requirements for the material and workmanship of a first-class 
structure, but in our opinion the working stresses given are in excess of good 
practice. 

Second —That the steel manufactured for this structure is first-class 
bridge material and in accordance with the specifications. 

Third —That the workmanship of this structure is first-class and in 
accordance with the requirements of the specifications. 

Fourth —That the erection and field riveting of the structure appears to 
have been done in a first-class manner. 

Fifth —That the actual sections of the various members agree with 
the sections ordered on the working drawings and shown on our sheets Nos. 
8 and 9, and that the shipping weights are correct. 

Sixth —That the members of floor systems are safe for the specified 
local live loads. 


> 


6 o 


0 


Seventh —That the following unit stresses in the main truss members, 


vi z : 


Tension nickel steel bars. 

Tension structural steel bars and riveted members 
Compression structural steel up to L/R = 20. . 
Compression structural steel for L/R above 20. . 


Lbs. Per 
Square Inch. 

30,000 

20,000 

19,000 

20,000-50 L/R 


are the limit of safety for the direct stresses from the sum of the live 
and dead loads, as the secondary and snow load stresses heretofore referred 
to will add to these unit stresses and thereby increase the actual unit 
stresses. 

Eighth —That the main truss members will not carry all the specified 
live loads for which this structure was designed. 

Ninth —That the structure can safely carry a considerable live load in 
addition to its actual dead load. 

As we, therefore, do not think the structure can carry all the specified 
live loads and vet is safe for considerable live load, we have tried to arrive 
at the actual live load which may safely come on this structure, using actual 
moving loads now in use on the subway, elevated, and surface lines of the 
city. 

The heaviest trolley car now actually in use in this city has four axles 
with a loaded weight of 15,500 lbs. on each axle, and an over-all length 
of 42 ft. 6 in., giving an average load of 1,460 lbs. p.l.f. of each trolley 

track. The heaviest elevated or subway “ motor ” car has two loaded axles 

r 

of 30,800 lbs. each, and two loaded axles of 22,200 lbs. each, and an over¬ 
all length of 51 ft., giving an average load of 2,080 lbs. p.l.f. track. The 
heaviest elevated or subway “ trailer ” car has four loaded axles of 17,500 
lbs. each and an over-all length of 51.4 ft., giving an average load of 1,360 
lbs. p.l.f. track. 

The average weight of an elevated or subway train made up of five 
motor cars and three trailer cars is thus found to be 1,810 lbs. p.l.f. track. 

The specified live load for the main trusses is one hundred pounds 
per sq. ft. on the roadways, and seventy-five pounds per sq. ft. on the foot- 
walks, and while we believe such loads are proper for designing local mem¬ 
bers of the floor system and secondary truss members, they are undoubtedly 








6i 


excessive for the main truss members, as no such load can possibly come 
on the entire width of the roadway and sidewalks .for any considerable 
length of the structure. For the main truss members, we, therefore, con¬ 
sider a live load of fifty pounds per square foot on the roadway and side¬ 
walks to be fully sufficient. 

By trial, we find that the main trusses will safely carry a live load of 
three thousand pounds per lineal foot of each truss, if the dead load be 
1 educed by one thousand pounds per lineal foot of each truss. Some of 
this dead load, consisting of the outer sidewalk stringers, floor-beam brack¬ 
ets, sidewalk gratings, and track material for the railway tracks on the 
upper deck has never been put on the structure, and some of the dead 
load now on, can be omitted, thus decreasing the full dead load and per¬ 
mitting the use of the above live load. Furthermore, the average live 
load on the trolley tracks can be reduced by regulating the minimum spaces 
between same, as these units are so small that for the main trusses the 
load is practically uniform for the cars spaced at reasonable intervals. For 
the elevated railway tracks it is not possible to greatly reduce the effective 
load per lineal foot by regulating the intervals between trains, as these 
trains are long and heavy units, and if trains are spaced at intervals of 
three or more train lengths, they will fall in such positions as to practically 
produce the maximum stresses in important parts of the structure. 

With these live loads, the roadway and footwalks produce a live load 
of 1794 ft.+ii ft.=28^4 ft.@50 lbs.—1,437 lbs. per lineal foot of truss, and 
if we assume each trolley track to be loaded with cars at clear intervals 
of one car length or about 85 ft. c. to c., they will produce a live load of 
2x730 lbs.=1,460 lbs. per lineal foot of truss, making a total live load of 
2,897 lbs. per lineal foot of truss, which would require a reduction in the 
dead load of about 1,000 lbs. per lineal foot of truss to meet the conditions 
of safety, and this reduction can be readily made. 

We, therefore, come to the conclusion that it is safe to run the four 
lines of trolley cars on this bridge as at present constructed, if the por¬ 
tions of the dead load not yet in place, and not required for highway or 
trolley service, be omitted, and if the four lines of inside track stringers 
on the upper deck be removed. 


62 


The “ additional ” dead load then will consist of the following items: 

Lbs. p. 1 . f. 
bridge. 


Concrete sub-pavement of roadway. 3 ’ 20 ° 

Wood block sub-pavement of roadway. L040 

Rails & conductor rails for 4 trolley tracks. 3/4 

Concrete footwalk slabs . 800 

6 railings . 4°6 

Electric wires, gas mains, etc. 160 


5.980 


Less deduction for removing 4 lines of stringers 


680 


5-3°o 

t 

or 2,650 lbs. p. 1. f. each truss, which is a reduction of 1,000 lbs. p. 1. f. 
each truss from the full assumed dead load. 

It will be noted that the concrete footwalk slabs are here taken 
at 800 lbs. p. 1. f., whereas they were taken at 500 lbs. p. 1. f. in the full 
dead load; this is due to the fact that in the completed structure they are 
intended to be 10 wide, whereas those now temporarily placed on the 
outer lines of railway stringers are 16' wide. To reach the full reduc¬ 
tion required, it will also be noted that we have reduced the allowance 
for wires and pipes to 160 lbs. p. 1. f. bridge. 

With a live load of 50 lbs. per square foot on the roadway and 
footwalks, and a live load of 780 lbs. per lineal^foot of each trolley track 
(which is equivalent to running trolley cars at intervals of 80 feet c. to c.) 
we get a total live load of 3,000 lbs. per lineal foot of each truss, and 
with this live load in addition to the total assumed dead load reduced 
by 1,000 lbs. per lineal foot of truss, we have made the complete stress 
sheet herewith submitted (Sheet No. 7) and it will be seen that all these 
stresses come practically within the limits of safety set by us, and the 
bridge is in our opinion safe for these loads. 

It will be noted that the dead load stresses shown on this stress 
sheet are computed with the full weight of structural material shown on 
our sheets 1, 2 and 3, but the total dead panel loads shown on our sheets 












63 


i to 6 inclusive were reduced for computing these dead load stresses by 
a uniform deduction of 1,000 lbs. p. 1. f. truss, as above itemized. 

The dead load of the floor systems can be further reduced if neces¬ 
sary, and we are of the opinion that by reducing the dead loads on all 
the lever arms, and perhaps increasing the dead loads on the Island span 
and anchor arms, the structure can be made to safely carry one pair of 
elevated tracks. 

In our opinion the most practical method of getting this bridge into 
prompt service is to remove the stringers from the two inside lines of 
upper railway tracks, and open the bridge for service of the highway, 
sidewalks and four trolley tracks immediately. 

If at some future time it is found necessary to make use of one pair of 
elevated tracks, further modifications of the dead loads can be made and 
the outer lines of elevated railway stringers used for their true purpose; 
the sidewalks being removed to their final position outside the trusses. 

We therefore make the following 

Recommendations : 

First —That the stringers of the two inside tracks on the upper deck, 
or other equivalent dead load, be removed to lighten the dead load. 

Second —That the trolley traffic be so regulated that if four tracks are 
in use the cars shall not run with clear intervals between them of less than 
their own length. 

Third —That the bridge be opened for the traffic of the sidewalks, high¬ 
way and four lines of trolley tracks as at present constructed, subject to the 
above recommendations. 

Fourth —That if any other moving loads be added to the structure, 
such further modifications of the dead load shall first be made as will keep 
the total direct stresses caused by the live and dead loads within the safe 
limits herein set. 

Under these recommendations we are confident the structure is per¬ 
fectly safe. 

Respectfully submitted, 

Boller & Hodge, 

Consulting Engineers. 


October 28, 1908. 


6 4 


Accompanied by one appendix and ten drawings, as follows: 

1. Detailed dead panel loads, Manhattan Anchor and Lever Arm. 

2. Detailed dead panel loads, Island Span and Lever Arms. 

3. Detailed dead panel loads, Queens Anchor and Lever Arm. 

4. Dead panel loads and points of application, Manhattan Anchor and' 

Lever Arms. 

5. Dead panel loads and points of application, Island Span and Lever 

Arms. 

6. Dead panel loads and points of application, Queens Anchor and 

Lever Arms. 

7. General stress sheet of main trusses. 

8. Sections of truss members, Manhattan and Queens Anchor and 

Lever Arms. 

9. Sections of truss members, Island Span and Lever Arms. 

10. Erection stress sheet. 

APPENDIX. 

Formulae for Determining the Stresses in tiie Rocker Arms of the 

Blackwells Island Bridge. 



Let PR = stress in the right rocker arm. 

Let di = deflection of point L37 of the Manhattan lever arm, due to 
a load of unity at L37, the rocker arm being considered disconnected at 
the bottom end. 

Let d2 = deflection of point L37 (the bottom of the left rocker arm) 
of the Blackwell’s Island west lever arm, due*to a load of unity at L37, the 
rocker arms being considered disconnected at their bottom ends. 

Let d3 = deflection of point L91 (the bottom of the right rocker arm) 
of the Blackwell’s Island east lever arm, due to a load of unity at L91, the 
rocker arms being considered disconnected at their bottom ends. 

Let d 4 = deflection of point L91 of the Queens lever arm due to a 
load of unity at L91, the rocker arm being considered disconnected at the 
bottom end. 










6 S 


Let (I20 deflection of point L 37 of the Blackwell’s Island West lever 
aim due to a load of unity at L 91, both rocker arms being disconnected 
at their bottom ends. 

Let d30=deflection of point L 91 of the Blackwell’s Island East lever 
arm due to a load of unity at L 37, both rocker arms being disconnected 
at their bottom ends. 

Let Di=deflection of point L 37 of the Manhattan lever arm, due to 
the given loading, the bottom end of the rocker arm being considered dis¬ 
connected. 

Let D2=deflection of point L 37 of the Blackwell’s Island West lever 
arm, due to the given loading, both rocker arms being considered discon¬ 
nected at their bottom ends. 

Let D3=deflection of point L 91 of the Blackwell’s Island East lever 
arm, due to the given loading, both rocker arms being considered discon¬ 
nected at their bottom ends. 

Let D4=deflection of point L 91 of the Queens lever arm, due to the 
given loading, the bottom end of the rocker arm being considered discon¬ 
nected. 

The above deflections it will be noted are all for bottom chord points. 

The deflections for the Manhattan and Queens anchor and lever arms 
should always include that due to the anchor bars. 

The deflections for the Blackwell’s Island anchor and lever arms should 
include that due to the rocker arms. 

The rocker arms L and R if disconnected at their bottom ends divide 
the structure into three portions, which are each statically determinate. 
These three portions we will designate as Part I, Part II and Part III. 

Part I. we will divide into Section No. 1, Manhattan Anchor Arm, 
and Section No. 2, Manhattan Lever Arm. 

Part II. we will divide into Section No. 3, Blackwell’s Island West 
Lever Arm, and Section No. 4, Blackwell’s Island Span, and Section No. 
5, Blackwell’s Island East Lever Arm. 

Part III. we will divide into Section No. 6, Queens Lever Arm, and 
Section No. 7, Queens Anchor Arm. 

Parts I. and II. When the rocker arm L is connected move up and 
down together and the bottom end of L, which is a common point for 
both parts,, has the same motion. 


66 


Parts II. and III. When the rocker arm R is connected move lip and 
down together, and the bottom end of R which is a common point for 
both parts has the same motion. 

It is also true that with a live load on Part I. and L and R connected, 
the members of Part I. can only receive stress from the load and from 
the rocker arm stress PL produced by this load, the members of Part 
II. can only receive stress from the stresses PL and PR and the members 
of Part III. can only receive stress from the stress PR. 

For a live load on Part II.: 

The stresses in Part I. are due to PL. 

The stresses in Part II. are due to the load and PL. and PR. 

The stresses in Part III. are due to PR. 

For a live load on Part III.: 

The stresses in Part I. are due to PL. 

The stresses in Part II. are due to PL. and PR. 

The stresses in Part III. are due to PR. and the load. 

A careful analytical determination of the several deflections shows that: 

A vertical downward force of unity will make di, d2, d3, d4, cLo 
and CI30, all downward. 

A vertical downward live load in Section No. 1 will make Di, up¬ 
ward. 

A vertical downward live load in Section No. 2 will make Di, 
downward. 

A vertical downward live load in Section No. 3 will make D2, 
downward, and D3, downward. 

A vertical downward live load in Section No. 4 will make D2, up¬ 
ward, and D3, upward. 

A vertical downward live load in Section No. 5 will make P>2, 
downward, and D3, downward. 

A vertical downward live load in Section No. 6 will make D4, 
downward. 

A vertical downward live load in Section No. 7 will make D4, 
upward. 

We may now write equations for the stresses PL and PR in terms of 
known quantities (PL and PR will be taken as in tension or plus until their 
sign is known). 


67 


lake first a load on Section No. i. We know that the motion of 
the bottom ends of both L and R is upward. 

The upward motion of L (bottom end) for section No. 2 is= 
Di+PLdi. 

the upward motion of L (bottom end) for section No. 3 is = 
—PLd2—PRd2o. 

These must be equal .*. Di+PLdi = — PLd2 — PRd2o or PL(di+d2) 
= —Di—PRd 20 . 

The upward motion of R (bott. end) for section No. 5 is= — 
PRd3—PLd3o. 

The upward motion of R (bott. end) for section No. 6 is = PRdq. 

These must be equal .*. —PRd3—PLd30=*PRd4 or PR(d3+d4) = 
—PLd30. 

Take now a load on section No. 2. We know that the motion of 
the bottom ends of both L & R is downward. 

The downward motion of L (bott. end) for section No. 2 =Di— 
PLdi. 

The downward motion of L (bott. end) for section No. 3 = PLd2+ 
PRd20. 

These must be equal .*. Di—PLdi=PLd2+PRd20 or PL(di4-d2) = 
Di—PRd 20 . 

The downward motion of R (bott. end) for section No. 5=PRd3 
4- PLd30. 

The downward motion of R (bott. end) for section No. 6 = — PRd4. 

These must be equal.*. PRd3 + PLd30 = — PRd4 or PR(d3 + d4) = 
— PLd30. 

Take now a load on Section No. 3. We know that the motion of the 
bottom ends of L and R is downward. 

The downward motion of L (bott. end) for section No. 2 = — PLdi. 

The downward motion of L (bott. end) for section No. 3 = D2 4- 
PLd2 4- PRd20. 

These must be equal .-. — PLdi = D2 4- PLd 2 4- PRd20 or PL(di + 
d2) = — D 2 — PRd20. 

The downward motion of R (bott. end) for section No. 5 = 034- 

PRd3 4- PLd30. 


68 


The downward motion of R (bott. end) for section No. 6 — — PRdq. 

These must be equal .-. D3 + PRd3 4- PLd30 = — PRd4 or PR(d3 + 
< 4 ) = — D3 — PLd30. 

Take now a load on section No. 4. We know that the motion of the 
bottom ends of L and R is upward. 

The upward motion of L (bottom end) for section No. 2=PLdi. 

The upward motion of L (bottom end) for section No. 3 = D2—PLd2— 
PRd20. 

These must be equal.-. PLdi=D2—PLd2—PRd20 or PL (di+d2) = 
D2—PRd20. 

The upward motion of R (bottom end) for section No. —PRd3— 

PLd30. 

The upward motion of R (bottom end) for section No. 6=PRd4. 

These must be equal.-. D3—PRd3—PLd30=PRd4 or PR (d3+d4) = 
D3—PLd30. 

For a load on each of the three remaining sections, we may write two 
simultaneous equations for finding PL and PR. 

For a load on section No. 5, we have: 

PL (di+d2) = —D2—PRd20. 

PR (d3+d4) = — D3—PLd30. 

For a load on section No. 6, we have: 

PL (di+d2) = — PRd2o. 

PR (d3+d4) = D4—PLd30. 

For a load on section No. 7, we have: 

PL (di+d2) = — PRd20. 

PR (d3+d4) = — D4—PLd30. r 

The above seven pairs of equations may be very much simplified by solv¬ 
ing them for PL and PR. 

The solved equations are: 

For a load on section No. 1, PL = — M Di. 

PR = +NDi. 

For a load on section No. 2, PL = +M Di. 

PR — _NDi. 

For a load on Section No. 3, PL = — M D2 + N D3. 

PR = — G D3 + ND2. 


69 


For a load on Section No. 4, PL = + M D2 — N D3. 

PR = + G D3 — N D2. 

For a load on Section No. 5, PL = — MD2 + N D3. 

PR = — G D 3 + N D2. 

For a load on Section No. 6, PL = — N D4. 

PR = + G D4. 

For a load on Section No. 7, PL = + N D4. 

PR = — G D4. 

In which M = d34-d4 

(di-f-d2) (d3 -)-d4)—d20d30 

G = di-}-d2 

(di-fd2) (d3~|-d4)--d2od3o 

N = d20 = d30 

(di-f-d2) (d3-fd4) — d20d30 (d 1 -j-d2) (d3-j-d4)—d2od30 

The numerical values of the deflections should be used in the above 

formulae without regard to their signs. 

The resultant signs for the solved equations will give the character of 

stress in the rocker arms; + indicating tension, and — compression. 

It will be noted that the values M. G. and N. are constants for the 

structure, so that they can be computed once for all and used for any and 

every position of the moving load. 










































































































































































































































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